\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14 - Algebraic Kernel
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AlgebraicKernel_d_2::SquareFreeFactorize_2 Concept Reference
Algebraic Kernel Reference » Concepts » Bivariate Algebraic Kernel

Definition

Computes a square free factorization of an AlgebraicKernel_d_2::Polynomial_2.

A polynomial \( p\) is factored into square free and pairwise coprime non-constant factors \( q_i\) with multiplicities \( m_i\) and a constant factor \( c\), such that \( p = c \cdot q_1^{m_1} \cdot ... \cdot q_n^{m_n}\).

The factor multiplicity pairs \( <q_i,m_i>\) are written to the given output iterator. The constant factor \( c\) is not computed.

Refines:

Assignable

CopyConstructible

See also
AlgebraicKernel_d_2::IsSquareFree_2
AlgebraicKernel_d_2::MakeSquareFree_2

Operations

template<class OutputIterator >
OutputIterator operator() (const AlgebraicKernel_d_2::Polynomial_2 &p, OutputIterator res)
 Copies in the output iterator the factors of a square free factorization of \( p\), with their multiplicity, as objects of type std::pair<AlgebraicKernel_d_2::Polynomial_2, AlgebraicKernel_d_2::Multiplicity_type>.